The Kâ characteristic X-ray line for tungsten has a wavelength of 1.94 10-11 m. What is the difference in energy between the two energy levels that give rise to this line? Express this in each of the following units.
(a) joules
(b) electron volts
To calculate the energy difference between the two energy levels that give rise to the Kâ characteristic X-ray line for tungsten, we can use the equation:
ΔE = hc/λ
where:
ΔE represents the energy difference,
h is the Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light (3 x 10^8 m/s), and
λ is the wavelength (1.94 x 10^-11 m).
(a) To express the energy difference in joules, we'll substitute the given values into the equation:
ΔE = (6.626 x 10^-34 J·s)(3 x 10^8 m/s) / (1.94 x 10^-11 m)
Calculating this expression will give us the energy difference in joules.
(b) To express the energy difference in electron volts (eV), we need to convert from joules to electron volts. We know that 1 eV is equal to 1.602 x 10^-19 J. So, we can use the following conversion:
1 eV = 1.602 x 10^-19 J
By dividing the energy difference in joules by this conversion factor, we can find the energy difference in electron volts.